Chapter 1.2B, Problem 20A

Starting with $1$ and $1$ as the first two terms of the Fibonacci sequence, answer the following.

a. Check that $F_1+F_3=F_4$

b. Compute $F_1+F_3+F_5$. The sum is which term?

c. Compute $F_1+F_3+F_5+F_7$. The sum is which term?

d. Write a conjecture based on the examples in parts (a), (b), and (c).